Ah, yes the battle of Britain. Let's have a look before that.
In the battle of Dunkirk Hitler let 338.000 Allied soldiers "let go" and were fleeing to Britain. He could have captured and imprisoned them but he didn't, he hoped to achieve a piece treaty with Britain to end the war. Big mistake it turned out.
Hitler had never any dissent with England quite the contrary he admired and respected them and never wanted to go to war with England.
Britain was in a disastrious situation and many politicians were prepared at that time for a peace treaty.
But Winston with his famous speach
We shall fight on the beaches (let's say a speech with a pokerface on) and the euphoria from the english people over the miracle "rescue".
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In it he tried to temper the national euphoria engendered by this seemingly miraculous delivery (almost the entire army was rescued, a feat thought most improbable beforehand), and send a message to the rest of the world that there would be no negotiated settlement.
The battle of Britain was a first major defeat for the wehrmacht, I would not say key turning point, not for the Germans anyhow but credit to the Brits and its Allies (especially the many Polish pilots) for the battle victory.
With the shift to the eastern front then (attack on Russia) and with the help of the US (lend lease) Britain began to rebuild its military forces.
Without that help and especially with the entry of the US in 41' into the war it would have not been possible much longer for Britain to stay in the war, as this quote from Winston speaks for itself:
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"This (the American declaration of war) is what I dreamed of, aimed at and worked for and now it has come to pass." - Winston Churchill, 15th February, 1942i